Abstract

It is convenient to measure the optical attenuation A of
the combination of a layer of atmospheric particulate matter and the
quartz fiber filter on which it has been collected. The problem of
relating A to the absorption and scattering coefficients
k and s of the particulate matter itself is
treated as a problem in diffuse reflectance spectroscopy using the
Kubelka–Munk theory. The results show that although, in general,
A is a nonlinear function strongly dependent on both
s and k, for a limited range of s and
sample thickness d, A can be a practically linear function
of k. Fortunately, this range includes that common to
atmospheric particulate samples. Furthermore, it is shown that if
the filter’s reflectance is sufficiently high, A can be
nearly independent of s. This is in agreement with
experimental and, for the limiting case when the substrate filter
reflectance is unity, theoretical results obtained by other
researchers. Use of such measurements of A as a means of
determining the black carbon mass loading C on a filter is
also investigated. It is shown that when the black carbon mass
fraction fc is high, as it is for samples
collected in large urban areas, A is a predictable and
practically linear function of C. However, when
fc is low, as it is for many rural locations,
then the slope of the function A(C) is strongly
dependent on fc, leading to possible
overestimates of C. This problem can be alleviated by
making the measurement of A at near-infrared wavelengths
rather than in the visible spectrum.

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